If r, s, and t are different odd numbers greater than 1, wha

[hazelnut01]

If r, s, and t are different odd numbers greater than 1, what is the median of r, s, and t?

1) rs=15
2) r+s+t=19

Source : Math Revolution
Official Answer : A

[DavidG@VeritasPrep]

If r, s, and t are different odd numbers greater than 1, what is the value of the median of r, s, and t?

1) rs=15
2) r+s+t=19

Source : Math Revolution
Official Answer : A

(I tweaked the question to make it clear that we need to find the value of the median, rather than to determine which of the variables is the median.)


Statement 1: the factors of 15: 1, 3, 5, 15. Because no variable can equal 1, we know that r and s will have to be 3 and 5. (Though we don't know which is which. Either r = 3 and s = 5 or r = 5 and s = 3.) So our set looks like this 3, 5, ___. Notice that we don't need to know the last term. The median has to be 5, as the last term must be a unique odd integer and cannot be 1. Because there is a unique value for the median, statement 1 alone is sufficient.

Statement 2: Case 1: r =3 s = 5 t = 11; median = 5
Case 2: r = 3, s = 7, t = 9; median = 7.
Different possibilities, so not sufficient.

The answer is A

[Brent@GMATPrepNow]

If r, s, and t are different odd numbers greater than 1, what is the median of r, s, and t?

1) rs=15
2) r+s+t=19

Target question: What is the median of r, s, and t?

Given: r, s, and t are different odd numbers greater than 10

Statement 1: rs = 15
Since r and s are odd numbers greater than 1, we know that one value is 3 and the other value is 5.
Since r, s, and t are different odd numbers greater than 1, we know that t does not equal 1, 3 or 5. So, t must be an odd number greater than 5.
So, our three values (r, s and t) look like this {3, 5, some odd integer greater than 5}
We can see that the median of this set MUST BE 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r+s+t = 19
Hmmm, if r, s and t are DIFFERENT ODD integers (greater than 1), in how many ways can their sum = 19?
This requires some testing.
Here are two possible scenarios:
Case a: the numbers are {3, 5, 11}. The sum = 19. In this case the median = 5
Case b: the numbers are {3, 7, 9}. The sum = 19. In this case the median = 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

[hoppycat]

Difficulty rating = ?
Sorry to keep asking but it helps me a lot

[DavidG@VeritasPrep]

Difficulty rating = ?
Sorry to keep asking but it helps me a lot

I'd advise against devoting too much energy to trying to determine difficulty levels. On the test, you won't know. What's easy for you, might not be for other test-takers, and vice versa. Experimental questions are mixed in. All you care about is answering the question correctly.

(But, if I had to guess, and I do, I'd say 600-ish.)

[Jay@ManhattanReview]

What is the answer if the question is changed to the following?

If r, s, and t are different odd numbers less than 15, what is the median of r, s, and t?

1) rs=15
2) r+s+t=19

-Jay
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